On your first character, this should be your priority:
(1) Unlock World Quests.
This requires you to get to friendly with the 3 main leveling factions and doing the 3 foothold quests for the War Campaign.
Once you’ve done this on one character, your other characters will be able to unlock world quests as soon as they hit 120 without needing the rep. (They also technically don’t need the footholds, but without them, you can’t get to the other continent, so they are worth doing. The foothold quests take 15-30 minute each.)
(2) Gear up a bit, as the next step will be super painful below ilvl 360 or so. Just running normal dungeons will drop ilvl 400 gear, and world quests sometimes reward gear. World quest gear rewards scale with your gear level up to about ilvl 420. So, as you get better gear, the rewards will get better. You can also look for some pieces on the Auction House if you’ve got extra gold, or to fill in stuborn spots.
(3) Open up Naz’jatar. You want to do this as soon as you can, but as mentioned above, it’s really rough at lower gear levels. An early quest rewards an ilvl 370 weapon, which is helpful.
After you open it up, Magni will show up with a quest. This quest chain unlocks essences, significantly increases the ilvl of you neck, and sets it’s AP level to 50. So, you’ll want to do this ASAP.
Early on in Naz’jatar, you’ll get a quest to upgrade a piece of Benthic gear. You can hold off on completing that quest and use the 20 manapearls they give you for the upgrade for 4 ilvl 385 gear tokens instead, which is generally the better use of the pearls early on for gearing for a new player.
Benthic tokens are Bind on Account, so it’s probably worth it to spend some time in Naz’jatar on your first character collecting pearls. (You’ll need to get rep there anyhow if you want to unlock flying, so I’d clear out the world quests there each day until you’re revered. By that time you’ll have lots of benthic tokens and pearls to buy more.) Starting off your alts with all your armor slots at 385 will make their lives a lot easier.
(3) Start the 8.3 content. The starter quest for this will pop up once you’ve unlocked essences the next time you’re in Boralas (or if you relog.) The opening quests are rough at lower gear levels, so you may want to gear up a bit in Naz’jatar first. (I’d at least go far enough in Naz’jatar to get the 4 pieces of Benthic gear I mentioned above before starting this content.